Back-of-the-envelope estimation in HLD - Scalability & System Analysis

Scalability Analysis - Back-of-the-envelope estimation

Growth Table: What Changes as Users Increase

Users	Requests per Second (RPS)	Data Storage	Network Bandwidth	Compute Needs
100	10-50 RPS	MBs	Low (Mbps)	Single server
10,000	1,000-5,000 RPS	GBs	Moderate (100s Mbps)	Multiple servers, load balancer
1,000,000	100,000+ RPS	TBs	High (Gbps)	Distributed servers, caching, sharding
100,000,000	10M+ RPS	Petabytes	Very High (multiple Gbps)	Massive distributed system, CDNs, microservices

First Bottleneck

At small scale (100 users), the server CPU and memory handle all requests easily.

At medium scale (10K users), the database becomes the first bottleneck due to query load.

At large scale (1M users), network bandwidth and database storage I/O limit performance.

At very large scale (100M users), data partitioning and global distribution become critical.

Scaling Solutions

• Vertical scaling: Upgrade server CPU, RAM, and storage for small scale.
• Horizontal scaling: Add more servers behind load balancers to share traffic.
• Caching: Use in-memory caches (like Redis) to reduce database load.
• Database read replicas: Distribute read queries to replicas to reduce master load.
• Sharding: Split database by user or data ranges to scale writes and storage.
• Content Delivery Network (CDN): Cache static content closer to users to reduce bandwidth.
• Asynchronous processing: Offload heavy tasks to background workers.

Back-of-Envelope Cost Analysis

Example for 10,000 users:

• Assuming 1,000 RPS peak.
• Each request ~100 KB data -> 100 MB/s bandwidth (~800 Mbps).
• Storage: 10 GB user data + logs per day.
• Database QPS: 1,000 queries per second, requiring a powerful DB server or replicas.
• Servers: 3-5 app servers with load balancer for redundancy.

Interview Tip

Start by estimating user numbers and request rates.

Calculate rough bandwidth and storage needs.

Identify the first bottleneck logically (usually database).

Suggest scaling solutions step-by-step, explaining why each helps.

Keep numbers simple and explain assumptions clearly.

Self Check Question

Your database handles 1,000 QPS. Traffic grows 10x to 10,000 QPS. What do you do first and why?

Key Result

Back-of-the-envelope estimation helps predict system needs and bottlenecks early, guiding practical scaling steps like caching, read replicas, and sharding as user traffic grows.

Practice

1. What is the main purpose of back-of-the-envelope estimation in system design?

easy

A. To quickly estimate system requirements using simple calculations

B. To write detailed code for the system

C. To create a full architecture diagram

D. To perform in-depth performance testing

Solution

1. Step 1: Understand the goal of back-of-the-envelope estimation

   This method is used to quickly guess system needs without detailed work.

2. Step 2: Compare options to the goal

   Only To quickly estimate system requirements using simple calculations matches the quick estimation purpose; others are detailed tasks.

3. Final Answer:

   To quickly estimate system requirements using simple calculations -> Option A

4. Quick Check:

   Quick estimation = To quickly estimate system requirements using simple calculations [OK]

Hint: Focus on quick, simple calculations for early guesses [OK]

Common Mistakes:

• Confusing estimation with detailed design
• Thinking it involves coding or testing
• Assuming it requires full diagrams

2. Which of the following is the correct way to start a back-of-the-envelope estimation for a web service's daily traffic?

easy

A. Calculate exact user behavior with detailed logs

B. Estimate average users per hour and multiply by 24

C. Design the database schema first

D. Write the full API specification

Solution

1. Step 1: Identify the starting point for traffic estimation

   Back-of-the-envelope estimation uses simple averages, not detailed data.

2. Step 2: Evaluate options for simplicity and relevance

   Estimate average users per hour and multiply by 24 uses average users per hour times 24 hours, a simple and effective start.

3. Final Answer:

   Estimate average users per hour and multiply by 24 -> Option B

4. Quick Check:

   Simple average x time = Estimate average users per hour and multiply by 24 [OK]

Hint: Use simple averages and multiply by time units [OK]

Common Mistakes:

• Starting with detailed logs instead of rough estimates
• Jumping to design before estimating traffic
• Confusing estimation with specification writing

3. You estimate a system will have 10,000 users daily, each making 5 requests on average. What is the total number of requests per day?

medium

A. 100,000 requests

B. 2,000 requests

C. 15,000 requests

D. 50,000 requests

Solution

1. Step 1: Multiply users by requests per user

   10,000 users x 5 requests each = 50,000 requests.

2. Step 2: Confirm total requests per day

   The total is simply the product of users and requests per user.

3. Final Answer:

   50,000 requests -> Option D

4. Quick Check:

   Users x requests = 50,000 [OK]

Hint: Multiply users by average requests per user [OK]

Common Mistakes:

• Adding instead of multiplying
• Mixing up users and requests
• Choosing an option too large or too small

4. A designer estimated 1 million requests per day but forgot to consider peak hour traffic. What is the likely problem with this estimation?

medium

A. Ignoring average request size affecting storage needs

B. Overestimating total daily traffic causing wasted resources

C. Underestimating peak load leading to potential system overload

D. Not including user authentication time

Solution

1. Step 1: Understand the impact of ignoring peak traffic

   Peak traffic is often much higher than average, so ignoring it underestimates load.

2. Step 2: Identify the consequence of underestimation

   System may overload during peak times if capacity is based on average only.

3. Final Answer:

   Underestimating peak load leading to potential system overload -> Option C

4. Quick Check:

   Ignoring peak = underestimation risk [OK]

Hint: Always consider peak, not just average, traffic [OK]

Common Mistakes:

• Assuming daily average covers peak needs
• Confusing storage with traffic load
• Focusing on unrelated factors like authentication time

5. You need to estimate the storage required for a photo-sharing app. Each photo is 3MB, and you expect 500,000 uploads per month. What is the approximate monthly storage needed?

hard

A. 1.5 TB

B. 150 GB

C. 15 GB

D. 1.5 GB

Solution

1. Step 1: Calculate total storage in MB

   500,000 photos x 3 MB each = 1,500,000 MB.

2. Step 2: Convert MB to TB

   1,500,000 MB ÷ 1024 ≈ 1465 GB ÷ 1024 ≈ 1.43 TB, approximately 1.5 TB.

3. Final Answer:

   1.5 TB -> Option A

4. Quick Check:

   Uploads x size ≈ 1.5 TB [OK]

Hint: Multiply count by size, then convert units [OK]

Common Mistakes:

• Forgetting to convert MB to GB
• Mixing up MB and GB units
• Using wrong multiplication factors